Compare Estimated and User Defined ITR"
In evalITR: Evaluating Individualized Treatment Rules

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "../man/figures/README-"
  )

library(dplyr)
library(evalITR)

load("../data/star.rda")

# specifying the outcome
outcomes <- "g3tlangss"

# specifying the data (remove other outcomes)
star_data <- star %>% 
  dplyr::select(-c(g3treadss,g3tmathss)) %>%
  mutate(SCHLURBN = as.numeric(SCHLURBN)) %>%
  rename(T = treatment)

star_data = star_data %>% mutate(
  cov1 = GKWHITE,
  cov2 = GKBUSED,
  cov3 = GKFRLNCH,
  school_urban = SCHLURBN
)

# specifying the formula
user_formula <- as.formula(
  "g3tlangss ~ T + gender + race + birthmonth + 
  birthyear + SCHLURBN + GRDRANGE + GKENRMNT + cov3 + 
  cov2 + cov1 ")

Estimated vs. User Defined ITR

The package allows to compare the performance of estimated ITRs with user defined ITRs. The estimate_itr function takes the following arguments:

| Argument | Description | |:-------- | :------------------------| | fit | a fitted object from the estimate_itr function | | user_itr | a function defined by users that returns a unit-level continuous score for treatment assignment (we assume those that have score less than 0 should not have treatment) | | data | a data frame | | treatment | a character string specifying the treatment variable in the data | | outcome | a character string specifying the outcome variable in the data | | budget | a numeric value specifying the maximum percentage of population that can be treated under the budget constraint |

The function returns an object that contains the estimated GATE, ATE, and AUPEC for the user defined ITR.

# estimate ITR 
fit <- estimate_itr(
  treatment = "T",
  form = user_formula,
  data = star_data,
  algorithms = c("causal_forest"),
  budget = 0.2,
  split_ratio = 0.7)

# user's own ITR
score_function <- function(data){
  data %>% 
    mutate(score = case_when(
      school_urban == 1 ~ 0.1, # inner-city
      school_urban == 2 ~ 0.2, # suburban
      school_urban == 3 ~ 0.4, # rural
      school_urban == 4 ~ 0.3, # urban
    )) %>%
    pull(score) -> score

  return(score)
}

# evalutate ITR
compare_itr <- evaluate_itr(
  fit = fit,
  user_itr = score_function,
  data = star_data,
  treatment = "T",
  outcome = outcomes,
  budget = 0.2)

# summarize estimates
summary(compare_itr)

We plot the estimated Area Under the Prescriptive Effect Curve (AUPEC) for the writing score across a range of budget constraints for user defined ITR and estimated ITRs. The plot shows that the estimated ITRs have better performance than the user defined ITR.

# plot the AUPEC 
plot(compare_itr)

Existing Model vs. User-Defined Model

The package also allows to compare the performance of estimated ITRs of existing ML packages with user defined models. The following code shows an example using causal forest from the grf package with sample splitting. The estimate_itr function takes the following arguments:

| Argument | Description | |:-------- | :------------------------| | treatment | a character string specifying the treatment variable in the data | | form | a formula specifying the outcome and covariates | | data | a data frame | | algorithms | a character vector specifying the ML algorithms to be used | | budget | a numeric value specifying the maximum percentage of population that can be treated under the budget constraint | | split_ratio | a character string specifying the outcome variable in the data | | user_model | a character string specifying the user defined model |

The user_model input should be a function that takes two arguments: training_data and test_data. The function will make use of the training_data to fit a model and then use the test_data to estimate CATE or other metrics of interest. It should also specify the way to get the ITR, based on the estimated effects.

In the following example, we fit a linear model with sample splitting and use the estimated CATE. We compute the ITR by assigning treatment to those with positive CATE and no treatment to those with negative CATE. The function user_model takes in the training data and test data and return a list that contains (1) an ITR; (2) a fitted model; and (3) a continuous score with the same length as the input data.

# user-defined model
user_model <- function(training_data, test_data){

  # model fit on training data
  fit <- train_model(training_data)

  # estimate CATE on test data
  compute_hatf <- function(fit, test_data){

    score <- fit_predict(fit, test_data)  
    itr   <- score_function(score)

    return(list(itr = itr, score = score))
  }

  hatf <- compute_hatf(fit, test_data)

  return(list(
    itr = hatf$itr, 
    fit = fit, 
    score = hatf$score))
}

Note that the user defined model can be any model that returns a unit-level continuous score for treatment assignment. It does not have to be a linear model or model that estimate CATE. We can specify custom functions in the train_model function and the fit_predict function to compute the score. If the model does not have a default predict function, we need to write up a custom function with fit_predict.

# train model
train_model <- function(data){
  fit <- lm(
    Y ~ T*(cov1 + cov1 + cov3), 
    data = data)
  return(fit)
}

# predict function
fit_predict <- function(fit, data){
  # need to change this function if 
  # the model does not have a default predict function
  score <- predict(fit, data) 
  return(score)
}

In addition, we can also choose any scoring rule that maps the score to a binary indicator of treatment assignment.

# score function
score_function <- function(score){
  itr <- (score >= 0) * 1
  return(itr)
}

If split_ratio is specified, the function will split the data into training and test data. The split_ratio should be a numeric value between 0 and 1. Alternatively, if n_folds is specified, the function will use the entire data to fit the user defined model via cross-validation.

# estimate ITR
compare_fit <- estimate_itr(
  treatment = "T",
  form = user_formula,
  data = star_data,
  algorithms = c("causal_forest"),
  budget = 0.2,
  split_ratio = 0.7,
  user_model = "user_model")


# evaluate ITR 
compare_est <- evaluate_itr(compare_fit)

# summarize estimates
summary(compare_est)
plot(compare_est)